Question

In the following figure, an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take π = 3.14). 

 

Answer 1

We have to find the area of the shaded portion. We have`ΔABC`which is an equilateral triangle and`AB=6 cm`. Let r be the radius of the circle.

We have O as the circumcentre.

`∠OBA=30°`

So, 

`Cos (30°)=3/r`

Thus, r=`2sqrt3`

So area of the shaded region,

=Area of the circle-ar(ΔABC)

`=(3.14)(2sqrt3)^2-sqrt3/4(6)^2`

`=(37.68-15.59)cm^2`

`= 22.126cm^2`